Magnetics: JEE Advanced - Physics, Solution by DC Pandey NEET Notes | EduRev

 Page 1


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  A uniform current carrying ring of mass m and radius R is connected by a massless string as 
shown. A uniform magnetic field B
0
 exist in the region to keep the ring in horizontal
 
position, then 
the current in the ring is 
 
 (a) 
0
mg
RB ?
   (b) 
0
mg
RB
   (c) 
0
mg
3 RB ?
   (d) 
2
0
mg
RB ?
 
Q 2.  A wire of mass 100 g is carrying a current of 2 A towards increasing x in the form of y - x
2
 (-2m = 
x = +2m). This wire is placed in a magnetic field tesla. 
ˆ
B 0.02k ??
?
. The acceleration of the wire 
(in m/s
2
) is 
 (a) 
ˆ
1.6 j ?   (b) 
ˆ
3.2 j ?   (c) 
ˆ
1.6 j   (d) zero 
Q 3.  A conductor of length l is placed perpendicular to a horizontal uniform magnetic field B. Suddenly 
a certain amount of charge is passed through it, when it is found to jump to a height h. The amount 
of charge that passes through the conductor is 
 (a) 
m gh
Bl
   (b) 
m gh
2Bl
   (c) 
m 2gh
Bl
   (d) None of these 
Q 4.  A solid conducting sphere of radius R and total charge q rotates about its diametric axis with 
constant angular speed The magnetic moment of the sphere is 
 (a) 
2
1
qR
3
?   (b) 
2
2
qR
3
?   (c) 
2
1
qR
5
?   (d) 
2
2
qR
5
? 
Q 5.  A charged particle moving along positive x-direction with a velocity v enters a region where there 
is a uniform magnetic field 
ˆ
B Bk ??
?
, from x = 0 to x = d. The particle gets deflected at an angle ?
 
from its initial path. The specific charge of the particle is 
 (a) 
Bd
v cos ?
   (b) 
v tan
Bd
?
   (c) 
Bsin
vd
?
   (d) 
vsin
Bd
?
 
Q 6.  A current carrying rod AB is placed perpendicular to an infinitely long current carrying wire as 
shown in figure. The point at which the conductor should be hinged so that it will not rotate (AC = 
CB) 
 
  (a) A       (b) somewhere between B and C 
  (c) C      (d) somewhere between A and C 
Page 2


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  A uniform current carrying ring of mass m and radius R is connected by a massless string as 
shown. A uniform magnetic field B
0
 exist in the region to keep the ring in horizontal
 
position, then 
the current in the ring is 
 
 (a) 
0
mg
RB ?
   (b) 
0
mg
RB
   (c) 
0
mg
3 RB ?
   (d) 
2
0
mg
RB ?
 
Q 2.  A wire of mass 100 g is carrying a current of 2 A towards increasing x in the form of y - x
2
 (-2m = 
x = +2m). This wire is placed in a magnetic field tesla. 
ˆ
B 0.02k ??
?
. The acceleration of the wire 
(in m/s
2
) is 
 (a) 
ˆ
1.6 j ?   (b) 
ˆ
3.2 j ?   (c) 
ˆ
1.6 j   (d) zero 
Q 3.  A conductor of length l is placed perpendicular to a horizontal uniform magnetic field B. Suddenly 
a certain amount of charge is passed through it, when it is found to jump to a height h. The amount 
of charge that passes through the conductor is 
 (a) 
m gh
Bl
   (b) 
m gh
2Bl
   (c) 
m 2gh
Bl
   (d) None of these 
Q 4.  A solid conducting sphere of radius R and total charge q rotates about its diametric axis with 
constant angular speed The magnetic moment of the sphere is 
 (a) 
2
1
qR
3
?   (b) 
2
2
qR
3
?   (c) 
2
1
qR
5
?   (d) 
2
2
qR
5
? 
Q 5.  A charged particle moving along positive x-direction with a velocity v enters a region where there 
is a uniform magnetic field 
ˆ
B Bk ??
?
, from x = 0 to x = d. The particle gets deflected at an angle ?
 
from its initial path. The specific charge of the particle is 
 (a) 
Bd
v cos ?
   (b) 
v tan
Bd
?
   (c) 
Bsin
vd
?
   (d) 
vsin
Bd
?
 
Q 6.  A current carrying rod AB is placed perpendicular to an infinitely long current carrying wire as 
shown in figure. The point at which the conductor should be hinged so that it will not rotate (AC = 
CB) 
 
  (a) A       (b) somewhere between B and C 
  (c) C      (d) somewhere between A and C 
Q 7.  The segment AB of wire carrying current I
1
 is placed perpendicular to a long straight wire carrying 
current I
2
 as shown in figure. The magnitude of force experienced by the straight wire AB is 
 
 (a) 
0 1 2
II
ln 3
2
?
?
   (b) 
0 1 2
II
ln 2
2
?
?
   (c) 
0 1 2
2 I I
2
?
?
   (d) 
0 1 2
II
2
?
?
 
Q 8.  A straight long conductor carries current along the positive x-axis. Identify the correct statement 
related to the four points A(a, a, 0), B(a, 0, a), C(a,-a, 0) and D(a, 0,-a). 
  (a) The magnitude of magnetic field at all points is same 
  (b) Fields at A and B are mutually perpendicular 
  (c) Fields at A and C are antiparallel  
  (d) All of the above 
Q 9.  The figure shows two coaxial circular loops 1 and 2, which forms same solid angle ? at point O. If 
B
1
 and B
2
 are the magnetic fields produced at the point O due to loop 1 and 2 respectively, then 
 
 (a) 
1
2
B
1
B
?   (b) 
1
2
B
2
B
?   (c) 
1
2
B
8
B
?   (d) 
1
2
B
4
B
? 
Q 10.  In the figure shown, a charge q moving with a velocity v along the x-axis enter into a region of 
uniform magnetic field. The minimum value of v so that the charge
 
q is able to enter the region x 
> b 
 
 (a) 
qBb
m
   (b) 
qBa
m
   (c) 
qB(b a)
m
?
   (d) 
qB(b a)
2m
?
 
Q 11.  An insulating rod of length l carries a charge q uniformly distributed on it. The rod is pivoted at 
one of its ends and is rotated at a frequency f about a fixed perpendicular axis. The magnetic 
moment of the rod is 
 (a) 
2
qfl
12
?
   (b) 
2
qfl
2
?
   (c) 
2
qfl
6
?
   (d) 
2
qfl
3
?
 
Page 3


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  A uniform current carrying ring of mass m and radius R is connected by a massless string as 
shown. A uniform magnetic field B
0
 exist in the region to keep the ring in horizontal
 
position, then 
the current in the ring is 
 
 (a) 
0
mg
RB ?
   (b) 
0
mg
RB
   (c) 
0
mg
3 RB ?
   (d) 
2
0
mg
RB ?
 
Q 2.  A wire of mass 100 g is carrying a current of 2 A towards increasing x in the form of y - x
2
 (-2m = 
x = +2m). This wire is placed in a magnetic field tesla. 
ˆ
B 0.02k ??
?
. The acceleration of the wire 
(in m/s
2
) is 
 (a) 
ˆ
1.6 j ?   (b) 
ˆ
3.2 j ?   (c) 
ˆ
1.6 j   (d) zero 
Q 3.  A conductor of length l is placed perpendicular to a horizontal uniform magnetic field B. Suddenly 
a certain amount of charge is passed through it, when it is found to jump to a height h. The amount 
of charge that passes through the conductor is 
 (a) 
m gh
Bl
   (b) 
m gh
2Bl
   (c) 
m 2gh
Bl
   (d) None of these 
Q 4.  A solid conducting sphere of radius R and total charge q rotates about its diametric axis with 
constant angular speed The magnetic moment of the sphere is 
 (a) 
2
1
qR
3
?   (b) 
2
2
qR
3
?   (c) 
2
1
qR
5
?   (d) 
2
2
qR
5
? 
Q 5.  A charged particle moving along positive x-direction with a velocity v enters a region where there 
is a uniform magnetic field 
ˆ
B Bk ??
?
, from x = 0 to x = d. The particle gets deflected at an angle ?
 
from its initial path. The specific charge of the particle is 
 (a) 
Bd
v cos ?
   (b) 
v tan
Bd
?
   (c) 
Bsin
vd
?
   (d) 
vsin
Bd
?
 
Q 6.  A current carrying rod AB is placed perpendicular to an infinitely long current carrying wire as 
shown in figure. The point at which the conductor should be hinged so that it will not rotate (AC = 
CB) 
 
  (a) A       (b) somewhere between B and C 
  (c) C      (d) somewhere between A and C 
Q 7.  The segment AB of wire carrying current I
1
 is placed perpendicular to a long straight wire carrying 
current I
2
 as shown in figure. The magnitude of force experienced by the straight wire AB is 
 
 (a) 
0 1 2
II
ln 3
2
?
?
   (b) 
0 1 2
II
ln 2
2
?
?
   (c) 
0 1 2
2 I I
2
?
?
   (d) 
0 1 2
II
2
?
?
 
Q 8.  A straight long conductor carries current along the positive x-axis. Identify the correct statement 
related to the four points A(a, a, 0), B(a, 0, a), C(a,-a, 0) and D(a, 0,-a). 
  (a) The magnitude of magnetic field at all points is same 
  (b) Fields at A and B are mutually perpendicular 
  (c) Fields at A and C are antiparallel  
  (d) All of the above 
Q 9.  The figure shows two coaxial circular loops 1 and 2, which forms same solid angle ? at point O. If 
B
1
 and B
2
 are the magnetic fields produced at the point O due to loop 1 and 2 respectively, then 
 
 (a) 
1
2
B
1
B
?   (b) 
1
2
B
2
B
?   (c) 
1
2
B
8
B
?   (d) 
1
2
B
4
B
? 
Q 10.  In the figure shown, a charge q moving with a velocity v along the x-axis enter into a region of 
uniform magnetic field. The minimum value of v so that the charge
 
q is able to enter the region x 
> b 
 
 (a) 
qBb
m
   (b) 
qBa
m
   (c) 
qB(b a)
m
?
   (d) 
qB(b a)
2m
?
 
Q 11.  An insulating rod of length l carries a charge q uniformly distributed on it. The rod is pivoted at 
one of its ends and is rotated at a frequency f about a fixed perpendicular axis. The magnetic 
moment of the rod is 
 (a) 
2
qfl
12
?
   (b) 
2
qfl
2
?
   (c) 
2
qfl
6
?
   (d) 
2
qfl
3
?
 
Q 12.  A wire carrying a current of 3 A is bent in the form of a parabola y
2
 = 4 - x as shown in figure, 
where x and y are in metre. The wire is placed in a uniform magnetic field 
ˆ
B 5k ?
?
tesla. The force 
acting on
 
the wire is 
 
 (a) 
ˆ
60i N   (b) 
ˆ
60i N ?   (c) 
ˆ
30i N   (d) 
ˆ
30i N ? 
Q 13.  An equilateral triangle frame PQR of mass M and side a is kept under the influence of magnetic 
force due to inward perpendicular magnetic field B and gravitational field as shown in the figure. 
The magnitude and direction of current in the frame so that
 
the frame remains at rest is 
 
 (a) 
2Mg
I ;anticlockwise
aB
?    (b) 
2Mg
I ;clockwise
aB
? 
  (c) 
Mg
I ;anticlockwise
aB
?    (d) 
Mg
I ;clockwise
aB
? 
Q 14.  A tightly-wound long solenoid has n turns per unit length, radius r and carries a current i. A 
particle having charge q and mass m is projected from a point on the axis in the direction 
perpendicular to the axis. The maximum speed for which particle does not strike the solenoid will 
be 
 (a) 
0
qrni
2m
?
   (b) 
0
qrni
m
?
   (c) 
0
2 qrni
3m
?
   (d) None of these 
Q 15.  If the acceleration and velocity of a charged particle moving in a constant magnetic region is given 
by 
1 2 1 2
ˆ ˆ ˆ ˆ
a a i a k, v b i b k ? ? ? ?
? ?
.
 
[a
1
 ,a
2
, b
1
 and b
2
 are constants], then choose the wrong statement 
  (a) Magnetic field may be along y-axis (b) a
1
b
1
 +a
2
b
2
 = 0 
  (c) Magnetic field is along x-axis  (d) Kinetic energy of particle is always constant 
Q 16.  A simple pendulum with a charged bob is oscillating as shown in the figure. Time period of 
oscillation is T and angular amplitude is ?. If a uniform magnetic field perpendicular to the plane 
of oscillation is switched on, then 
 
  (a) T will decrease but ? will remain constant (b) T will remain constant but ? will decrease 
  (c) Both T and ? will remain the same  (d) Both T and ? will decrease 
Page 4


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  A uniform current carrying ring of mass m and radius R is connected by a massless string as 
shown. A uniform magnetic field B
0
 exist in the region to keep the ring in horizontal
 
position, then 
the current in the ring is 
 
 (a) 
0
mg
RB ?
   (b) 
0
mg
RB
   (c) 
0
mg
3 RB ?
   (d) 
2
0
mg
RB ?
 
Q 2.  A wire of mass 100 g is carrying a current of 2 A towards increasing x in the form of y - x
2
 (-2m = 
x = +2m). This wire is placed in a magnetic field tesla. 
ˆ
B 0.02k ??
?
. The acceleration of the wire 
(in m/s
2
) is 
 (a) 
ˆ
1.6 j ?   (b) 
ˆ
3.2 j ?   (c) 
ˆ
1.6 j   (d) zero 
Q 3.  A conductor of length l is placed perpendicular to a horizontal uniform magnetic field B. Suddenly 
a certain amount of charge is passed through it, when it is found to jump to a height h. The amount 
of charge that passes through the conductor is 
 (a) 
m gh
Bl
   (b) 
m gh
2Bl
   (c) 
m 2gh
Bl
   (d) None of these 
Q 4.  A solid conducting sphere of radius R and total charge q rotates about its diametric axis with 
constant angular speed The magnetic moment of the sphere is 
 (a) 
2
1
qR
3
?   (b) 
2
2
qR
3
?   (c) 
2
1
qR
5
?   (d) 
2
2
qR
5
? 
Q 5.  A charged particle moving along positive x-direction with a velocity v enters a region where there 
is a uniform magnetic field 
ˆ
B Bk ??
?
, from x = 0 to x = d. The particle gets deflected at an angle ?
 
from its initial path. The specific charge of the particle is 
 (a) 
Bd
v cos ?
   (b) 
v tan
Bd
?
   (c) 
Bsin
vd
?
   (d) 
vsin
Bd
?
 
Q 6.  A current carrying rod AB is placed perpendicular to an infinitely long current carrying wire as 
shown in figure. The point at which the conductor should be hinged so that it will not rotate (AC = 
CB) 
 
  (a) A       (b) somewhere between B and C 
  (c) C      (d) somewhere between A and C 
Q 7.  The segment AB of wire carrying current I
1
 is placed perpendicular to a long straight wire carrying 
current I
2
 as shown in figure. The magnitude of force experienced by the straight wire AB is 
 
 (a) 
0 1 2
II
ln 3
2
?
?
   (b) 
0 1 2
II
ln 2
2
?
?
   (c) 
0 1 2
2 I I
2
?
?
   (d) 
0 1 2
II
2
?
?
 
Q 8.  A straight long conductor carries current along the positive x-axis. Identify the correct statement 
related to the four points A(a, a, 0), B(a, 0, a), C(a,-a, 0) and D(a, 0,-a). 
  (a) The magnitude of magnetic field at all points is same 
  (b) Fields at A and B are mutually perpendicular 
  (c) Fields at A and C are antiparallel  
  (d) All of the above 
Q 9.  The figure shows two coaxial circular loops 1 and 2, which forms same solid angle ? at point O. If 
B
1
 and B
2
 are the magnetic fields produced at the point O due to loop 1 and 2 respectively, then 
 
 (a) 
1
2
B
1
B
?   (b) 
1
2
B
2
B
?   (c) 
1
2
B
8
B
?   (d) 
1
2
B
4
B
? 
Q 10.  In the figure shown, a charge q moving with a velocity v along the x-axis enter into a region of 
uniform magnetic field. The minimum value of v so that the charge
 
q is able to enter the region x 
> b 
 
 (a) 
qBb
m
   (b) 
qBa
m
   (c) 
qB(b a)
m
?
   (d) 
qB(b a)
2m
?
 
Q 11.  An insulating rod of length l carries a charge q uniformly distributed on it. The rod is pivoted at 
one of its ends and is rotated at a frequency f about a fixed perpendicular axis. The magnetic 
moment of the rod is 
 (a) 
2
qfl
12
?
   (b) 
2
qfl
2
?
   (c) 
2
qfl
6
?
   (d) 
2
qfl
3
?
 
Q 12.  A wire carrying a current of 3 A is bent in the form of a parabola y
2
 = 4 - x as shown in figure, 
where x and y are in metre. The wire is placed in a uniform magnetic field 
ˆ
B 5k ?
?
tesla. The force 
acting on
 
the wire is 
 
 (a) 
ˆ
60i N   (b) 
ˆ
60i N ?   (c) 
ˆ
30i N   (d) 
ˆ
30i N ? 
Q 13.  An equilateral triangle frame PQR of mass M and side a is kept under the influence of magnetic 
force due to inward perpendicular magnetic field B and gravitational field as shown in the figure. 
The magnitude and direction of current in the frame so that
 
the frame remains at rest is 
 
 (a) 
2Mg
I ;anticlockwise
aB
?    (b) 
2Mg
I ;clockwise
aB
? 
  (c) 
Mg
I ;anticlockwise
aB
?    (d) 
Mg
I ;clockwise
aB
? 
Q 14.  A tightly-wound long solenoid has n turns per unit length, radius r and carries a current i. A 
particle having charge q and mass m is projected from a point on the axis in the direction 
perpendicular to the axis. The maximum speed for which particle does not strike the solenoid will 
be 
 (a) 
0
qrni
2m
?
   (b) 
0
qrni
m
?
   (c) 
0
2 qrni
3m
?
   (d) None of these 
Q 15.  If the acceleration and velocity of a charged particle moving in a constant magnetic region is given 
by 
1 2 1 2
ˆ ˆ ˆ ˆ
a a i a k, v b i b k ? ? ? ?
? ?
.
 
[a
1
 ,a
2
, b
1
 and b
2
 are constants], then choose the wrong statement 
  (a) Magnetic field may be along y-axis (b) a
1
b
1
 +a
2
b
2
 = 0 
  (c) Magnetic field is along x-axis  (d) Kinetic energy of particle is always constant 
Q 16.  A simple pendulum with a charged bob is oscillating as shown in the figure. Time period of 
oscillation is T and angular amplitude is ?. If a uniform magnetic field perpendicular to the plane 
of oscillation is switched on, then 
 
  (a) T will decrease but ? will remain constant (b) T will remain constant but ? will decrease 
  (c) Both T and ? will remain the same  (d) Both T and ? will decrease 
Q 17.  Magnetic field in a region is given by 
0
ˆ
B B xk ?
?
.
 
Two loops each of side a is placed in this 
magnetic region in the x-y plane with one of its sides onx-axis. If F
1
 is the force on loop 1 and F
2
 
be the force on loop 2, then 
 
  (a) F
1 
= F
2 
= 0   (b) F
1
 > F
2
   (c) F
2 
> F
1
   (d) F
1
 = F
2
 ? 0 
Q 18.  Consider a co-axial cable which consists of an inner wire of radius a surrounded by an outer shell 
of inner and outer radii b and c respectively. The inner wire carries a current I and outer shell 
carries an equal and opposite current. The magnetic field at a distance x from the axis where b < 
x< c is 
 (a) 
22
0
22
I(c b )
2 x(c a )
??
??
  (b) 
22
0
22
I(c x )
2 x(c a )
??
??
  (c) 
22
0
22
I(c x )
2 x(c b )
??
??
  (d) zero 
Q 19.  A particle of mass 1 × 10
-26
 kg and charge +1.6 × 10
-19
 C travelling with a velocity of 1.28 × 10
6
 
m/s along positive direction of x-axis enters a region in which a uniform electric field E
?
 
and a 
uniform magnetic field B
?
are present such that 
   E
z
 =-102.4 kV/m and B
y
 = 8 × 10
-2
 Wb/m
2
 
  The particle enters this region at origin at time t = 0. Then  
  (a) net force acts on the particle along the +ve z-direction 
  (b) net force acts on the particle along -ve z-direction 
  (c) net force acting on particle is zero 
  (d) net force acts in x-z plane 
Q 20.  A wire lying along y-axis from y = 0 to y = 1 m carries a current of 2 mA in the negative y-
direction. The wire lies in a non-uniform magnetic field given by 
ˆˆ
B (0.3T / m)yi (0.4Tm)yj ??
?
.
 
The magnetic force on the entire wire is 
 (a) 
4
ˆ
3 10 jN
?
??  (b) 
3
ˆ
6 10 k N
?
?  (c) 
4
ˆ
3 10 k N
?
??  (d) 
4
ˆ
3 10 k N
?
? 
Q 21.  A particle having a charge of 20 ?C and mass 20 ?g moves along a circle of radius 5 cm under the 
action of a magnetic field B = 0.1 tesla. When the particle is at P, uniform transverse electric field 
is switched on and it is found that the particle continues along the tangent with a uniform velocity. 
Find the electric field 
 
  (a) 2 V/m   (b) 0.5 V/m  (c) 5 V/m   (d) 1.5 V/m 
Q 22.  Two circular coils A and B of radius 
5
2
cm and 5 cm carry currents 5 A and 52
 
respectively. 
The plane of B is perpendicular to plane of A and their centres coincide. Magnetic field at the 
centre is 
Page 5


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  A uniform current carrying ring of mass m and radius R is connected by a massless string as 
shown. A uniform magnetic field B
0
 exist in the region to keep the ring in horizontal
 
position, then 
the current in the ring is 
 
 (a) 
0
mg
RB ?
   (b) 
0
mg
RB
   (c) 
0
mg
3 RB ?
   (d) 
2
0
mg
RB ?
 
Q 2.  A wire of mass 100 g is carrying a current of 2 A towards increasing x in the form of y - x
2
 (-2m = 
x = +2m). This wire is placed in a magnetic field tesla. 
ˆ
B 0.02k ??
?
. The acceleration of the wire 
(in m/s
2
) is 
 (a) 
ˆ
1.6 j ?   (b) 
ˆ
3.2 j ?   (c) 
ˆ
1.6 j   (d) zero 
Q 3.  A conductor of length l is placed perpendicular to a horizontal uniform magnetic field B. Suddenly 
a certain amount of charge is passed through it, when it is found to jump to a height h. The amount 
of charge that passes through the conductor is 
 (a) 
m gh
Bl
   (b) 
m gh
2Bl
   (c) 
m 2gh
Bl
   (d) None of these 
Q 4.  A solid conducting sphere of radius R and total charge q rotates about its diametric axis with 
constant angular speed The magnetic moment of the sphere is 
 (a) 
2
1
qR
3
?   (b) 
2
2
qR
3
?   (c) 
2
1
qR
5
?   (d) 
2
2
qR
5
? 
Q 5.  A charged particle moving along positive x-direction with a velocity v enters a region where there 
is a uniform magnetic field 
ˆ
B Bk ??
?
, from x = 0 to x = d. The particle gets deflected at an angle ?
 
from its initial path. The specific charge of the particle is 
 (a) 
Bd
v cos ?
   (b) 
v tan
Bd
?
   (c) 
Bsin
vd
?
   (d) 
vsin
Bd
?
 
Q 6.  A current carrying rod AB is placed perpendicular to an infinitely long current carrying wire as 
shown in figure. The point at which the conductor should be hinged so that it will not rotate (AC = 
CB) 
 
  (a) A       (b) somewhere between B and C 
  (c) C      (d) somewhere between A and C 
Q 7.  The segment AB of wire carrying current I
1
 is placed perpendicular to a long straight wire carrying 
current I
2
 as shown in figure. The magnitude of force experienced by the straight wire AB is 
 
 (a) 
0 1 2
II
ln 3
2
?
?
   (b) 
0 1 2
II
ln 2
2
?
?
   (c) 
0 1 2
2 I I
2
?
?
   (d) 
0 1 2
II
2
?
?
 
Q 8.  A straight long conductor carries current along the positive x-axis. Identify the correct statement 
related to the four points A(a, a, 0), B(a, 0, a), C(a,-a, 0) and D(a, 0,-a). 
  (a) The magnitude of magnetic field at all points is same 
  (b) Fields at A and B are mutually perpendicular 
  (c) Fields at A and C are antiparallel  
  (d) All of the above 
Q 9.  The figure shows two coaxial circular loops 1 and 2, which forms same solid angle ? at point O. If 
B
1
 and B
2
 are the magnetic fields produced at the point O due to loop 1 and 2 respectively, then 
 
 (a) 
1
2
B
1
B
?   (b) 
1
2
B
2
B
?   (c) 
1
2
B
8
B
?   (d) 
1
2
B
4
B
? 
Q 10.  In the figure shown, a charge q moving with a velocity v along the x-axis enter into a region of 
uniform magnetic field. The minimum value of v so that the charge
 
q is able to enter the region x 
> b 
 
 (a) 
qBb
m
   (b) 
qBa
m
   (c) 
qB(b a)
m
?
   (d) 
qB(b a)
2m
?
 
Q 11.  An insulating rod of length l carries a charge q uniformly distributed on it. The rod is pivoted at 
one of its ends and is rotated at a frequency f about a fixed perpendicular axis. The magnetic 
moment of the rod is 
 (a) 
2
qfl
12
?
   (b) 
2
qfl
2
?
   (c) 
2
qfl
6
?
   (d) 
2
qfl
3
?
 
Q 12.  A wire carrying a current of 3 A is bent in the form of a parabola y
2
 = 4 - x as shown in figure, 
where x and y are in metre. The wire is placed in a uniform magnetic field 
ˆ
B 5k ?
?
tesla. The force 
acting on
 
the wire is 
 
 (a) 
ˆ
60i N   (b) 
ˆ
60i N ?   (c) 
ˆ
30i N   (d) 
ˆ
30i N ? 
Q 13.  An equilateral triangle frame PQR of mass M and side a is kept under the influence of magnetic 
force due to inward perpendicular magnetic field B and gravitational field as shown in the figure. 
The magnitude and direction of current in the frame so that
 
the frame remains at rest is 
 
 (a) 
2Mg
I ;anticlockwise
aB
?    (b) 
2Mg
I ;clockwise
aB
? 
  (c) 
Mg
I ;anticlockwise
aB
?    (d) 
Mg
I ;clockwise
aB
? 
Q 14.  A tightly-wound long solenoid has n turns per unit length, radius r and carries a current i. A 
particle having charge q and mass m is projected from a point on the axis in the direction 
perpendicular to the axis. The maximum speed for which particle does not strike the solenoid will 
be 
 (a) 
0
qrni
2m
?
   (b) 
0
qrni
m
?
   (c) 
0
2 qrni
3m
?
   (d) None of these 
Q 15.  If the acceleration and velocity of a charged particle moving in a constant magnetic region is given 
by 
1 2 1 2
ˆ ˆ ˆ ˆ
a a i a k, v b i b k ? ? ? ?
? ?
.
 
[a
1
 ,a
2
, b
1
 and b
2
 are constants], then choose the wrong statement 
  (a) Magnetic field may be along y-axis (b) a
1
b
1
 +a
2
b
2
 = 0 
  (c) Magnetic field is along x-axis  (d) Kinetic energy of particle is always constant 
Q 16.  A simple pendulum with a charged bob is oscillating as shown in the figure. Time period of 
oscillation is T and angular amplitude is ?. If a uniform magnetic field perpendicular to the plane 
of oscillation is switched on, then 
 
  (a) T will decrease but ? will remain constant (b) T will remain constant but ? will decrease 
  (c) Both T and ? will remain the same  (d) Both T and ? will decrease 
Q 17.  Magnetic field in a region is given by 
0
ˆ
B B xk ?
?
.
 
Two loops each of side a is placed in this 
magnetic region in the x-y plane with one of its sides onx-axis. If F
1
 is the force on loop 1 and F
2
 
be the force on loop 2, then 
 
  (a) F
1 
= F
2 
= 0   (b) F
1
 > F
2
   (c) F
2 
> F
1
   (d) F
1
 = F
2
 ? 0 
Q 18.  Consider a co-axial cable which consists of an inner wire of radius a surrounded by an outer shell 
of inner and outer radii b and c respectively. The inner wire carries a current I and outer shell 
carries an equal and opposite current. The magnetic field at a distance x from the axis where b < 
x< c is 
 (a) 
22
0
22
I(c b )
2 x(c a )
??
??
  (b) 
22
0
22
I(c x )
2 x(c a )
??
??
  (c) 
22
0
22
I(c x )
2 x(c b )
??
??
  (d) zero 
Q 19.  A particle of mass 1 × 10
-26
 kg and charge +1.6 × 10
-19
 C travelling with a velocity of 1.28 × 10
6
 
m/s along positive direction of x-axis enters a region in which a uniform electric field E
?
 
and a 
uniform magnetic field B
?
are present such that 
   E
z
 =-102.4 kV/m and B
y
 = 8 × 10
-2
 Wb/m
2
 
  The particle enters this region at origin at time t = 0. Then  
  (a) net force acts on the particle along the +ve z-direction 
  (b) net force acts on the particle along -ve z-direction 
  (c) net force acting on particle is zero 
  (d) net force acts in x-z plane 
Q 20.  A wire lying along y-axis from y = 0 to y = 1 m carries a current of 2 mA in the negative y-
direction. The wire lies in a non-uniform magnetic field given by 
ˆˆ
B (0.3T / m)yi (0.4Tm)yj ??
?
.
 
The magnetic force on the entire wire is 
 (a) 
4
ˆ
3 10 jN
?
??  (b) 
3
ˆ
6 10 k N
?
?  (c) 
4
ˆ
3 10 k N
?
??  (d) 
4
ˆ
3 10 k N
?
? 
Q 21.  A particle having a charge of 20 ?C and mass 20 ?g moves along a circle of radius 5 cm under the 
action of a magnetic field B = 0.1 tesla. When the particle is at P, uniform transverse electric field 
is switched on and it is found that the particle continues along the tangent with a uniform velocity. 
Find the electric field 
 
  (a) 2 V/m   (b) 0.5 V/m  (c) 5 V/m   (d) 1.5 V/m 
Q 22.  Two circular coils A and B of radius 
5
2
cm and 5 cm carry currents 5 A and 52
 
respectively. 
The plane of B is perpendicular to plane of A and their centres coincide. Magnetic field at the 
centre is 
 (a) 0   (b) 
5
4 2 10 T
?
??  (c) 
5
4 10 T
?
??  (d) 
5
2 2 10 T
?
?? 
Q 23.  A charged particle with specific charge s moves undeflected through a region of space containing 
mutually perpendicular and uniform electric and magnetic fields E and B. When the electric field 
is switched off, the particle will move in a circular path of radius 
 (a) 
E
Bs
   (b) 
Es
B
   (c) 
2
Es
B
   (d) 
2
E
Bs
 
Q 24.  Two long parallel conductors are carrying currents in the same direction as shown in the figure. 
The upper conductor (A) carrying a current of 100 A is held firmly in position. The lower 
conductor (B)carries a current of 50 A and free to move up and down. The linear mass density of 
the lower conductor is 0.01 kg/m 
 
  (a) Conductor B will be in equilibrium if the distance between the conductors is 0.1 m 
  (b) Equilibrium of conductor B is unstable 
  (c) Both (a) and (b) are wrong 
  (d) Both (a) and (b) are correct 
Q 25.  Equal currents are flowing in three infinitely long wires along positive x, y and z directions. The 
magnetic field at a point (0,0, - a) would be (i = current in each wire) 
 (a) 
0
i
ˆˆ
( j i)
2a
?
?
?
   (b) 
0
i
ˆˆ
(i j)
2a
?
?
?
   (c) 
0
i
ˆˆ
(i j)
2a
?
?
?
   (d) 
0
i
ˆˆ
( i j)
2a
?
??
?
 
Q 26.  In the figure the force on the wire ABC in the given uniform magnetic field will be(B = 2 tesla)  
 
  (a) 4(3+2 ?)Nt  (b) 20 Nt  (c) 30 Nt  (d) 40 Nt  
Q 27.  A uniformly charged ring of radius R is rotated about its axis with constant linear speed v of each 
of its particles. The ratio of electric field to magnetic field at a point P on the axis of the ring 
distant x = R from centre of ring is (cis speed of light) 
 
 (a) 
2
c
v
    (b) 
2
v
c
   (c) 
v
c
    (d) 
c
v
 
Answers